from an Abstract published February 2015: Mental Illness, Mass Shootings, and the Politics of American Firearms,
Jonathan M. Metzl, MD, PhD and Kenneth T. MacLeish, PhD (Copyright © American Public Health Association 2015, Am J Public Health. 2015 February; 105(2): 240–249. doi: 10.2105/AJPH.2014.302242 PMCID: PMC4318286)
" ...Yet surprisingly little population-level evidence supports the notion that individuals diagnosed with mental illness are more likely than anyone else to commit gun crimes. According to Appelbaum,25 less than 3% to 5% of US crimes involve people with mental illness, and the percentages of crimes that involve guns are lower than the national average for persons not diagnosed with mental illness. Databases that track gun homicides, such as the National Center for Health Statistics, similarly show that fewer than 5% of the 120 000 gun-related killings in the United States between 2001 and 2010 were perpetrated by people diagnosed with mental illness.26"